Folding dynamics of Trp-cage in the presence of chemical interference and macromolecular crowding. I

Proteins fold and function in the crowded environment of the cell's interior. In the recent years it has been well established that the so-called "macromolecular crowding" effect enhances the folding stability of proteins by destabilizing their unfolded states for selected proteins. On the other hand, chemical and thermal denaturation is often used in experiments as a tool to destabilize a protein by populating the unfolded states when probing its folding landscape and thermodynamic properties. However, little is known about the complicated effects of these synergistic perturbations acting on the kinetic properties of proteins, particularly when large structural fluctuations, such as protein folding, have been involved. In this study, we have first investigated the folding mechanism of Trp-cage dependent on urea concentration by coarse-grained molecular simulations where the impact of urea is implemented into an energy function of the side chain and/or backbone interactions derived from the all-atomistic molecular dynamics simulations with urea through a Boltzmann inversion method. In urea solution, the folding rates of a model miniprotein Trp-cage decrease and the folded state slightly swells due to a lack of contact formation between side chains at the terminal regions. In addition, the equilibrium m-values of Trp-cage from the computer simulations are in agreement with experimental measurements. We have further investigated the combined effects of urea denaturation and macromolecular crowding on Trp-cage's folding mechanism where crowding agents are modeled as hard-spheres. The enhancement of folding rates of Trp-cage is most pronounced by macromolecular crowding effect when the extended conformations of Trp-cast dominate at high urea concentration. Our study makes quantitatively testable predictions on protein folding dynamics in a complex environment involving both chemical denaturation and macromolecular crowding effects.     

A lower bound for sums of eigenvalues of the Laplacian

Let be the th Dirichlet eigenvalue of a bounded domain in . According to Weyl's asymptotic formula we have

The optimal in view of this asymptotic relation lower estimate for the sums has been proven by P.Li and S.T.Yau (Comm. Math. Phys. 88 (1983), 309-318). Here we will improve this estimate by adding to its right-hand side a term of the order of that depends on the ratio of the volume to the moment of inertia of .

     

Local Lower Norm Estimates for Dyadic Maximal Operators and Related Bellman Functions

We provide lower \(L^{q}\) and weak \(L^{q}\)-bounds for the localized dyadic maximal operator on \(\mathbb {R}^{n}\), when the local \(L^{1}\) and the local \(L^{p}\) norms of the function are given. We actually do that in the more general context of homogeneous trees in probability spaces.     

Linear conic formulations for two-party correlations and values of nonlocal games

In this work we study the sets of two-party correlations generated from a Bell scenario involving two spatially separated systems with respect to various physical models. We show that the sets of classical, quantum, no-signaling and unrestricted correlations can be expressed as projections of affine sections of appropriate convex cones. As a by-product, we identify a spectrahedral outer approximation to the set of quantum correlations which is contained in the first level of the Navascués, Pironio and Acín (NPA) hierarchy and also a sufficient condition for the set of quantum correlations to be closed. Furthermore, by our conic formulations, the value of a nonlocal game over the sets of classical, quantum, no-signaling and unrestricted correlations can be cast as a linear conic program. This allows us to show that a semidefinite programming upper bound to the classical value of a nonlocal game introduced by Feige and Lovász is in fact an upper bound to the quantum value of the game and moreover, it is at least as strong as optimizing over the first level of the NPA hierarchy. Lastly, we show that deciding the existence of a perfect quantum (resp. classical) strategy is equivalent to deciding the feasibility of a linear conic program over the cone of completely positive semidefinite matrices (resp. completely positive matrices). By specializing the results to synchronous nonlocal games, we recover the conic formulations for various quantum and classical graph parameters that were recently derived in the literature.     

Quiescent and shear-induced crystallization of polyprophylenes

In this paper, the effect of shear on the flow-induced crystallization (FIC) of several polypropylenes of various macrostructures was studied using rheometry combined with polarized microscopy. Generally, an increase in strain and strain rate or decrease of temperature is found to decrease the thermodynamic barrier for crystal formation and thus enhancing crystallization kinetics at temperatures between the melting and crystallization points. Secondly, popular models based on suspension theory which are used to relate the degree of crystallinity to normalized rheological functions (such as viscosity) are validated experimentally. For this purpose, the space filling of crystals in the polarized micrographs determined from image processing was plotted as a function of normalized viscosity under various shear rates. It is found that the constant(s) of various suspension models should be dependent on the flow parameters in order for the suspension models to describe the effect of shear on FIC, particularly at higher shear rates.     

Development of an impedimetric immunosensor based on electropolymerized polytyramine films for the direct detection of Salmonella typhimurium in pure cultures of type strains and inoculated real samples

The development of a faradic impedimetric immunosensor based on electropolymerized polytyramine (Ptyr) films for the detection of S. typhimurium in milk is described for the first time. Polyclonal anti-Salmonella was cross-linked, in the presence of glutaraldehyde vapors, on Ptyr-modified gold electrodes. The dielectric behaviour of Ptyr films was evaluated with capacitance measurements, while their stability in neutral aqueous solutions was examined with impedimetric measurements. The effect of the concentration of tyramine in the forming solution on both the sensitivity and the dynamic range of the resulted immunosensors was also investigated. The alteration of the interfacial features of the electrodes due to different modification or recognition steps, was measured by faradic electrochemical impedance spectroscopy in the presence of a hexacyanoferrate(II)/(III) redox couple. At samples containing a low initial concentration of 10 cfu mL⁻¹S. typhimurium, that actually defines the LOD of the immunosensors, signal changes of 33% and 88% were achieved after 3 and 10 h incubation, respectively. To achieve the working simplicity expected by a biosensor, immunoreaction was performed directly in cultures. This resulted in the elimination of various centrifugation and washing steps, which are used for the isolation of bacteria cells from the culture, thus making the proposed immunosensors promising candidates for on-site applications. Finally, the proposed immunosensors were successfully used for the detection of S. typhimurium in experimentally inoculated milk samples.     

On weak type inequalities for dyadic maximal functions

We obtain sharp estimates for the localized distribution function of the dyadic maximal function , given the local L¹ norms of ? and of G○? where G is a convex increasing function such that G(x)/x→+∞ as x→+∞. Using this we obtain sharp refined weak type estimates for the dyadic maximal operator.     

Micellar and surface properties of a poly(methyl methacrylate)-block-poly(N-isopropylacrylamide) copolymer in aqueous solution

Critical micelle concentrations (cmc) of aqueous solutions of poly(methyl methacrylate)-block-poly(N-isopropylacrylamide) were determined at several temperatures by surface tensiometry. Below the lower critical solution temperature (LCST), the low Delta mic H 0 determined can be assigned to the PMMA block being tightly coiled in the dispersed molecular state, so that the unfavorable interactions of hydrophobic entities with water are minimized. Above the LCST the cmc value was found to increase; an anomalous behavior that can be directly related to the micelle-globule transition of the hydrophilic block. Interestingly, above the LCST the surface tension of relatively concentrated solutions was found to depend weakly on temperature not following the usual strong decrease with temperature expected for aqueous solutions.